Stabilized edge-based finite element simulation of free-surface flows

摘要

Free-surface flows occur in several problems in hydrodynamics, such as fuel or water sloshing in tanks, waves breaking in ships, offshore platforms, harbours and coastal areas. The computation of such highly nonlinear flows is challenging since free-surfaces commonly present merging, fragmentation and breaking parts, leading to the use of interface-capturing Eulerian approaches. In such methods the surface between two fluids is captured by the use of a marking function which is transported in a flow field. In this work we present a three-dimensional parallel edge-based incompressible SUPG/PSPG finite element method to cope with free-surface problems with volume-of-fluid (VOF) extensions to track the evolving free surface. The pure advection equation for the scalar marking function was solved by a fully implicit parallel edge-based SUPG finite element formulation. We studied variants of this formulation, considering the effects of discontinuity capturing and a particular tangent transformation designed to increase interface sharpness. Global mass conservation is enforced adding or removing mass proportionally to the absolute value of the normal velocity of the interface. We introduce a parallel dynamic deactivation algorithm to solve the marking function equation only in a small region around the interface. The implementation is targeted to distributed memory systems with cache-based processors. The performance and accuracy of the proposed solution method were tested with several validation problems.